5.1 Trigonometric Functions of Acute AnglesFri Oct 17

Do NowSolve for x

1) 1^2 + x^2 = 2^2

2) x^2 + x^2 = 1

Quiz Review

• Retakes by Monday

Trigonometric Ratios

• Given a right triangle, the lengths of the sides of the triangle are used to define the six trigonometric ratios

• Sine (Sin)• Cosine (Cos)• Tangent (Tan)• Cosecant (Csc)• Secant (Sec)• Cotangent (Cot)

Trigonometric Functions Values of an Acute Angle

• Let be an acute angle of a right triangle, then the 6 trig functions are:

Reciprocal Functions

• Cosecant, secant, and cotangent are reciprocals of sine, cosine, and tangent respectively

Ex1

• If sinx = 12/13, find the other 5 trig function values

Ex 2

• Given Tanx = 4/3, find the other 5 trig function values

Ex3

• If sinx = 6/7 and x is an acute angle, find the other 5 trig function values

Similar Triangles and Trig

• If two triangles are similar, their trigonometric function values will be the same

• Ex: 3-4-5 and 12-16-20 right triangles

• Note to self, if time keep going

Closure

• If cosx = 4/7, find the other 5 trig values

• HW: p.444 #1-29 odds

5.1 Trigonometric Functions of Acute AnglesMon Oct 20

• Do Now• Let cscx = 5/4 Find the other 5 trig values

HW Review: p.444 #1-15 odds

Trig Values of 30, 45, 60 deg

• Using geometry, we can construct right triangles using 30, 45, and 60 degrees, then find the trig values

30-60-90 Right Triangle

•

45-45-90 Right Triangle

•

Ex• As a hot-air balloon began to rise, the ground

crew drove 1.2 mi to an observation station. The initial observation from the station estimated the angle between the ground and line of sight to the balloon to be 30 degrees. Approximately how high was the balloon at that point?

Decimal-Degree and Degree-Minute-Second Form

• To convert from DMS to decimal degree,– 1) Use 2nd -> Angle to write degree and minute– 2) Use Alpha -> + sign to write second

• To convert from decimal degree to DMS,– Use 2nd -> Angle -> DMS

Ex

• Convert 72.18 degrees to DMS and back

Trig Values of other Angles

• To find the 6 trig values of other angles, we will use the calculator.

– Be sure your calculator is in the correct mode• Angles can be expressed in degrees or radians

– Round to at least 3 decimal places

Finding the Angle

• We use inverse trig functions (has a -1) to find the angle

• Ex: Find the angle whose sine value is 0.20113

Ex

• A paint crew has purchased new 30ft extension ladders. They extend the ladder to 25 ft and position the base 6.5 ft away from the wall. What angle does the ladder make with the ground?

Cofunction Identities

• Since the 2 acute angles in a right triangle will always be complementary, the following identities are a result

Ex

• Given sin 18 deg = 0.3090, cos 18 deg = 0.9511, and tan 18 deg = 0.3249, find the 6 trig function values of 72 degrees

Closure

• Given sin 8 deg = 0.1392, cos 8 deg = 0.9903, and tan 8 deg = 0.1405, find the 6 trig function values of 82 degrees

• HW: p.444 #31-101 odds

5.1 ReviewTues Oct 21

• Do Now• Evaluate in exact value• 1) csc 45 deg

• 2) cos 60 deg

HW Review: p.444 #17-101

Closure

• What are the 6 trig functions? What do they tell us?

• HW: none